We produce a family of new, non-arithmetic lattices in PU(2, 1). All previously known examples were commensurable with lattices constructed by Picard, Mostow, and Deligne– Mostow, and fell into 9 commensurability classes. Our groups produce 5 new distinct commensurability classes. Most of the techniques are completely general, and provide efficient geometric and computational tools for construc...

The comparative approach regarding the ethics of surrogacy from the Western secular and Islamic bioethical view reveals both commensurable and incommensurable relationship. Both are eager to achieve the welfare of the mother, child and society as a whole but the approaches are not always the same. Islamic bioethics is straightforward in prohibiting surrogacy by highlighting the lineage problem ...

Abstract We study the quasi-isometric rigidity of a large family finitely generated groups that split as graphs with virtually free vertex and two-ended edge groups. Let G be group is one-ended, hyperbolic relative to abelian subgroups, has JSJ decomposition over subgroups containing only are not quadratically hanging. Our main result any abstractly commensurable . In particular, our applies ce...

We construct an atlas of a gene expression databank, to visualize similarity relationships between expression data sets. Such an atlas could be used as an interface to the databank, for users searching for relevant background data or data for their own in-silico analyses. The two main research problems in constructing an atlas are (1) to preprocess the data to make different sets commensurable,...

Two manifolds are commensurable if they have diffeomorphic covers. We would like invariants that distinguish manifolds up to commensurability. A collection of such commensurability invariants is complete if it always distinguishes non-commensurable manifolds. Commensurability invariants of hyperbolic 3-manifolds are discussed in [NRe]. The two main ones are the invariant trace field and the inv...

Recall that hyperbolic 3-manifolds M and N are said to be commensurable if they have a common finite sheeted covering. This is equivalent to the fundamental groups having subgroups of finite index which are conjugate in PSL(2,C). In general it is very difficult to determine if two manifolds are commensurable or not, once the most obvious invariants of commensurability (for example, the invarian...

This paper proposes a Trust-Region Based Augmented Method (TRALM) to solve a combined Environmental and Economic Power Dispatch (EEPD) problem. The EEPD problem is a multi-objective problem with competing and non-commensurable objectives. The TRALM produces a set of non-dominated Pareto optimal solutions for the problem. Fuzzy set theory is employed to extract a compromise non-dominated sol...